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Optimal risk sharing as a cooperative game

Łukasz Kuciński (2011)

Applicationes Mathematicae

The problem of choosing an optimal insurance policy for an individual has recently been better understood, particularly due to the papers by Gajek and Zagrodny. In this paper we study its multi-agent version: we assume that insureds cooperate with one another to maximize their utility function. They create coalitions by bringing their risks to the pool and purchasing a common insurance contract. The resulting outcome is divided according to a certain rule called strategy. We address the fundamental...

Optimal stopping of a 2-vector risk process

Krzysztof Szajowski (2010)

Banach Center Publications

The following problem in risk theory is considered. An insurance company, endowed with an initial capital a > 0, receives insurance premiums and pays out successive claims from two kind of risks. The losses occur according to a marked point process. At any time the company may broaden or narrow down the offer, which entails the change of the parameters of the underlying risk process. These changes concern the rate of income, the intensity of the renewal process and the distribution of claims....

Optimal streams of premiums in multiperiod credibility models

L. Gajek, P. Miś, J. Słowińska (2007)

Applicationes Mathematicae

Optimal arrangement of a stream of insurance premiums for a multiperiod insurance policy is considered. In order to satisfy solvency requirements we assume that a weak Axiom of Solvency is satisfied. Then two optimization problems are solved: finding a stream of net premiums that approximates optimally 1) future claims, or 2) "anticipating premiums". It is shown that the resulting optimal streams of premiums enable differentiating between policyholders much more quickly than one-period credibility...

Optimality conditions for a class of mathematical programs with equilibrium constraints: strongly regular case

Jiří V. Outrata (1999)

Kybernetika

The paper deals with mathematical programs, where parameter-dependent nonlinear complementarity problems arise as side constraints. Using the generalized differential calculus for nonsmooth and set-valued mappings due to B. Mordukhovich, we compute the so-called coderivative of the map assigning the parameter the (set of) solutions to the respective complementarity problem. This enables, in particular, to derive useful 1st-order necessary optimality conditions, provided the complementarity problem...

Optimality of the replicating strategy for American options

Marek Kociński (1999)

Applicationes Mathematicae

The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox-Ross-Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an optimal replicating strategy that is not optimal in the global sense.

Optimisation de plans de financement immobiliers

Frédéric Gardi (2010)

RAIRO - Operations Research

La finance de marché est devenue un des domaines d'ap- plication privilégiés de la recherche opérationnelle. D'un autre côté, rares sont les applications touchant la banque de détail, tournée vers le grand public. Dans ce papier, nous abordons un problème d'actualité dans le secteur bancaire français : l'optimisation de plans de financement immobiliers. Le travail que nous présentons a été effectué dans le cadre du développement par la société Experian-Prologia d'une nouvelle application d'instruction...

Optimization of parameters in the Menzerath–Altmann law

Ján Andres, Lubomír Kubáček, Jitka Machalová, Michaela Tučková (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Four formulas of the Menzerath–Altmann law are tested from the point of view of their applicability and suitability. The accuracy of related approximations of measured data is examined by the least square method at first. Then the accuracy of calculated parameters in the formulas under consideration is compared statistically. The influence of neglecting parameter c is investigated as well. Finally, the obtained results are discussed by means of an illustrative example from quantitative linguistics....

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